An integrated DEMATEL Six Sigma hybrid framework for manufacturing process improvement

Abstract

Six Sigma is a widely practiced, systematic, and structured methodology embedded with statistical methods and managerial philosophies for quality improvement by large firms along with small firms in the industrialized economies. Application of Six Sigma in Micro Small Medium Enterprises (MSMEs) in developing economies is limited due to several barriers these firms face. In academic literature, there is unavailability of sufficient evidence of successful implementation of the practice in these firms to encourage and provide a roadmap for its implementation. Thus, there is a need for studies that presents frameworks with illustrative case studies demonstrating the implementation of Six Sigma in MSMEs. In the present times, MSME firms in developing economies are facing competition from world leaders, and thus it has become essential for them to focus on the quality of their manufacturing products and at the same time being productive and efficient. Moreover, in the literature, it is observed that the potential of operations research (OR) methods is not sufficiently explored in Six Sigma studies. OR-based methods and tools should be integrated into Six Sigma implementation frameworks as these methods expand the application portfolio and tackle some of the barriers that limit the application of Six Sigma in small-scale firms. In this paper, a Six Sigma implementation framework for an MSME organization is developed incorporating Multi Criteria Decision Making (MCDM) tool Decision-Making Trial and Evaluation Laboratory, apart from other conventional tools like cause and effect analysis, benefit effort analysis, Pareto analysis, control charts, etc. The proposed framework is illustrated in detail with the help of a real-life case study of an MSME in India. The results obtained after the implementation of this framework signify that the incorporation of MCDM in Six Sigma lead to a significant improvement in the sigma level of the firm despite of unavailability of sufficient resources.

Appendices

Appendix A

1.1 DEMATEL methodology

DEMATEL, an MCDM approach is utilized to classify the defects identified in the define phase into cause group and effect group based on whether they affect or are affected by others respectively (Govindan and Chaudhuri 2016). The detailed steps of the DEMATEL approach are given below (Zhou et al. 2018):

Step 1 Define quality feature and establish measurement scale.

The quality feature is a set of influential characteristics that impact the sophisticated system, which can be determined by literature review, brainstorming, and expert evaluation. After defining the influential characteristics in researching system, establish the measurement scale for the causal relationships and pairwise comparisons among influential characteristics. Four levels 0, 1, 2, 3 are suggested, respectively meaning “no impact”, “low impact”, “high impact,” and “extreme high impact”. In this step, factors and their direct relations are displayed by a weighted and directed graph.

Step 2 Extract the Direct Relation Matrix (DRM) of influential factors.

In this step, the transformation from the weighted and directed graph into DRM has been carried out. For n influential characteristics F₁, F₂, …, F_n, DRM is denoted as

$$ D = \left( {d_{ij} } \right)_{n \times n} (i,j = 1,2, \ldots ,n), $$

where $d_{ij}$ is the direct relation of F_i over F_j based on the measurement scale.

Step 3 Normalize the DRM.

Normalized direct relations of factors are a mapping from $d_{ij}$ to [0, 1], which is calculated as follows:

$$ N = \frac{D}{{\hbox{max} \left( {\sum\nolimits_{j} {d_{ij} } ,\sum\nolimits_{i} {d_{ij} } } \right)}} $$

Step 4 Calculate the Total Relations Matrix (TRM).

TRM contains direct and indirect relations among factors. The calculation of TRM through the normalized DRM can be done as follows:

$$ T = N\left( {E - N} \right)^{ - 1} $$

where $E$ is $n \times n$ identity matrix.

Step 5 Classify influential factors.

Based on the sum of each row R_i (i = 1, 2, …, n) and column C_i (i = 1, 2, …, n) of the TRM T_n×n, R_i + C_i and R_i − C_i can be obtained. R_i + C_i is defined as the prominence, indicating the importance of the ith influential factor. R_i − C_i classifies the ith influential factor as the cause (R_i − C_i > 0) or effect (R_i − C_i < 0) factor in researching system.

Appendix B

2.1 Construction of C&E Matrix

Cause and Effect matrix is a quality tool which helps the decision makers in identifying the causes and root causes of the problem based on customers’ preferences. The detailed steps for constructing a C&E matrix are given below (Lee et al. 2009):

Step 1 List down the outputs identified during SIPOC. These are our Key Process Output Variables (KPOVs). There should be no less than three outputs under O in SIPOC. Therefore, there will be no less than three outputs in C&E matrix.

Step 2 Rate these KPOVs according to customers’ preferences (X_i) using a scale from 1 to 10 with 1 representing least important and 10 representing most important.

Step 3 List the steps of the process as listed in SIPOC.

Step 4 List the Key Process Input Variables (KPIVs) for all the steps in the process found using fishbone diagram.

Step 5 Determine the correlation scores between KPOVs and KPIVs based on the scale defined in Table 8 (Y_ij).

Table 8 Scale for correlation scores

Step 6 Calculate the total score of each KPIV as given below

$$ Z_{j} = \sum\limits_{i} {X_{i} Y_{ij} } $$

and select top four as root causes for further improvements.

Appendix C

3.1 Construction of Benefit Effort Matrix

The benefit-effort matrix was designed specifically for the purpose of deciding which of the many suggested solutions to implement. It provides answers to the question of which solutions seem easiest to achieve with the most effects (Gijo and Sarkar 2013). The steps of construction of a benefit effort matrix are as follows:

Step 1 Retrieve suggested solutions through barnstorming or discussions.

Step 2 Ask the decision makers to rate each of the solution using a scale from 1 to 10 with 1 representing least important and 10 representing most important based on two factors, the benefit that can be obtained after the implementation of that solution and the cost that will be incurred during its implementation.

Step 3 Construct the benefit effort matrix by plotting effort rating on the horizontal axis and benefit ratings of the solution on the vertical axis and divide it into four quadrants namely, high effort-high benefit, high effort-lo benefit, low effort-high benefit and low effort-low benefit.

Appendix D

See the Tables 9, 10, 11 and 12.

Table 9 Direct relation matrix given by quality head

Table 10 Average direct relation matrix

Table 11 Normal direct relation matrix

Table 12 Total relation matrix

Appendix E

5.1 AHP Methodology

AHP is a powerful MCDM approach which is used to prioritize the alternatives based on some selected criteria. The detailed steps of the AHP approach is given below (Darbari et al. 2019):

Suppose there are n alternatives $A_{1} ,A_{2} , \ldots ,A_{n}$ and m criteria $C_{1} ,C_{2} , \ldots ,C_{m}$ whose importance weights need to be calculated with respect to a given goal ‘g’. The AHP method is employed as per the sequential steps given below:

Step 1 Pairwise-comparison.

The criteria are compared pair-wise on a scale of 1–9 representing subjective judgements for the levels of importance. The numeric values ‘1–3–5–7–9’ represent the “equally important-moderately important–important-very important–extremely important”, with the intermediate subjectivities represented by 2, 4, 6 and 8. This leads to construction of mxm matrix A = (a_ij) where a_ij is the numeric value of the pair-wise comparison of the ith and jth criteria in terms of how much criteria i dominates criteria j, following the mathematical rule

$$ a_{ij} = \frac{1}{{a_{ji} }},\quad a_{ii} = 1,\quad a_{ij} = \frac{{a_{ik} }}{{a_{jk} }} $$

Step 2 Normalization.

Normalize the matrix A by dividing each (i, j)th element (a_ij) by the jth column sum a_j to derive the matrix A* as shown below:

$$ A^{*} = \left[ {a_{ij}^{*} } \right] = \begin{array}{*{20}c} \; & {\begin{array}{*{20}c} {\;\;\;C_{1} \;\;\;\;\;\;\;\;\;C_{2} \;\;\;} & \; & \; & \; & {C_{m} } & \; \\ \end{array} } \\ {\begin{array}{*{20}c} {C_{1} } \\ {C_{2} } \\ . \\ . \\ . \\ {C_{m} } \\ \end{array} } & {\left[ {\begin{array}{*{20}c} {a_{11} /a_{1} } & {a_{12} /a_{2} } & {\begin{array}{*{20}c} . & . & . \\ \end{array} } & {a_{1m} /a_{m} } \\ {a_{21} /a_{1} } & {a_{22} /a_{2} } & {\begin{array}{*{20}c} . & . & . \\ \end{array} } & {a_{2m} /a_{m} } \\ {\begin{array}{*{20}c} . \\ . \\ . \\ \end{array} } & {\begin{array}{*{20}c} . \\ . \\ . \\ \end{array} } & {\begin{array}{*{20}c} . \\ . \\ . \\ \end{array} } & {\begin{array}{*{20}c} . \\ . \\ . \\ \end{array} } \\ {a_{m1} /a_{1} } & {a_{m2} /a_{2} } & {\begin{array}{*{20}c} . & . & . \\ \end{array} } & {a_{mm} /a_{m} } \\ \end{array} } \right]} \\ \end{array} $$

Step 3 Generate principal eigen vector.

Calculate the average a_i* of rows of the matrix A* to generate the priority vector (a₁*, a₂*,…. a_m*) which is the principal eigenvector of A. Since the priority vector is unique up to positive scalar multiplication, therefore the normalization of A is done to ensure the uniqueness of the vector of priorities. The principal eigen vector $y \in R^{n}$ corresponding to the maximum eigen value $\lambda_{\hbox{max} }$ is generated using the following equation: $A^{*} \lambda_{\hbox{max} } = \lambda y$.

Step 4 Check consistency.

The judgment must be checked for its consistency by utilizing the following equations:

$$ CI = \frac{{\lambda_{\hbox{max} } - n}}{n - 1},\quad CR = \frac{CI}{RI} $$

where CI is the Consistency Index, CR is the Consistency Ratio and RI is the Random Index whose value is taken as per the Table 13.

Table 13 Random index

The matrix with CR < 0.1 is acceptable, which implies that the overall inconsistency less than 10% is acceptable. Else, the judgment is reviewed and the steps are repeated till an acceptable consistency ratio is derived.

Step 5 Generate weights of alternatives.

The priorities of the criteria so obtained are used in the calculation of the weight of priorities of sub-criteria in the next level. This continues till the priority weights of alternatives are calculated. The rating of the alternatives is obtained by aggregating the relative priorities using the hierarchical additive weighting method.

Appendix F

See the Tables 14, 15, 16 and 17.

Table 14 Pairwise comparison matrix given by quality head

Table 15 Priority weights for each member

Table 16 Comparison matrix

Table 17 Pairwise comparison matrix with respect to viscosity